Total gas meter using speed of sound and velocity measurements

ABSTRACT

An apparatus is provided for measuring total gas content of a fluid flowing through a process line. The apparatus comprises a bleed line in fluid communication with the process line for bleeding a portion of the fluid from the process line at a bleed line pressure that is lower than the process line pressure. A speed of sound propagating through the fluid in the bleed line is determined and is, in turn, used to determine a gas volume fraction of the fluid in the bleed line. In one aspect, the total gas content of the fluid flowing through the process line is calculated as a function of the gas volume fraction of the fluid in the bleed line and a velocity of the fluid in the bleed line. In another aspect, the velocity of the fluid in the bleed line is adjusted to be approximately equal to a predetermined velocity. In yet another aspect, dissolved gas in the process fluid  13  is released before the gas content measurement point by applying a high intensity ultrasonic field to the fluid  13.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 60/616,504 filed Oct. 5, 2004 (Attorney Docket No.CC-0777PR) and U.S. Provisional Patent Application No. 60/601,919(Attorney Docket No. CC-0767PR) filed Aug. 16, 2004, both of which areincorporated by reference herein in their entirety.

BACKGROUND

The present invention generally relates to an apparatus for measuringtotal gas in a fluid flowing in a process line.

Entrained gases are gases that exist in a gaseous form, mixed in theprocess fluid. For many industrial applications with small, less than˜20% gas fraction by volume, the gas is typically in the form of smallbubbles contained in a liquid continuous mixture. Entrained gases existas either free bubbles moving within the stock or as bound (or residual)air that is adhered to the fiber. In either cases, entrained gas cangenerally be detected by monitoring the compressibility of the mixtureand correlating the compressibility to volumetric percentage ofentrained gas.

Dissolved gases are dissolved within the mixture on a molecular level.While in the solution, dissolved gases pose few operation problems.Typically dissolved gases have a negligible effect on thecompressibility of the mixture. Thus, dissolved gases are difficult todetect via compressibility measurements. The sum of the entrained gasesand the dissolved gases is defined as the total gases contained with aprocess mixture.

Monitoring levels of entrained and dissolved gases (e.g., air) isdesirable in many industrial processes. For example, entrained anddissolve gases in the approach system of paper making machines are oftenproblematic, leading to a wide variety of problems, including flow linepulsations, pin-holes in the produced paper, reduced paper sheetstrength, and excessive build-up of aerobic growths.

Although dissolved gases are typically not problematic while dissolved,problems arise when dissolved gases come out of a solution as a resultof either decreases in pressure or increases in temperature. One exampleof this is in pressurized head boxes on paper machines where thepressure drop associated with spraying the pulp/water mixture on to thepaper machine can cause dissolved gases to come out of the solution andform entrained gas.

Various technologies exist to monitor dissolved gases in a process line.Typically, such technologies require that a representative sample of theprocess fluid be expanded to atmospheric conditions to liberate thedissolved air in the fluid, and the resulting entrained air is measuredeither directly, as in entrained gas testers (EGTs), by weight of thede-aerated fluid, as in so-called “bird bath” arrangements, or byultrasonic measurement. While such technologies work well for someapplications, the accuracy of these technologies may be sensitive to thevelocity of the fluid. More specifically, as the velocity of the fluidsample is reduced, a situation is created wherein gas velocity isappreciably faster than liquid velocity (gas/liquid slip), resulting ina discrepancy between the actual dissolved air and the measureddissolved air. Thus, there remains a need for an accurate method ofmeasuring dissolved and total air in a process fluid.

SUMMARY OF THE INVENTION

The above described and other drawbacks and deficiencies are overcome oralleviated by an apparatus for measuring total gas content of a fluidflowing through a process line at a process line pressure, the apparatuscomprising a bleed line in fluid communication with the process line forbleeding a portion of the fluid from the process line at a bleed linepressure that is lower than the process line pressure. A devicedetermines a speed of sound propagating through the fluid flowingthrough the bleed line, and at least one processor: determines a gasvolume fraction of the fluid in the bleed line using the speed of sound,determines the total gas content of the fluid flowing through theprocess line using the gas volume fraction of the fluid in the bleedline and a velocity of the fluid in the bleed line, and provides anoutput signal indicative of the total gas content of the fluid flowingthrough the process line.

In another aspect, there is provided an apparatus for measuring totalgas content of a fluid flowing through a process line at a process linepressure. The apparatus comprises a bleed line in fluid communicationwith the process line for bleeding a portion of the fluid from theprocess line at a bleed line pressure that is lower than the processline pressure and at a bleed line velocity that is approximately equalto a predetermined velocity. A device determines a speed of soundpropagating through the fluid flowing through the bleed line, and atleast one signal processor: determines the total gas content of thefluid flowing through the process line as a gas volume fraction of thefluid in the bleed line using the speed of sound, and provides an outputsignal indicative of the total gas content of the fluid flowing throughthe process line.

In yet another aspect, a method for measuring total gas content of afluid flowing through a process line at a process line pressure isprovided. The method comprises: bleeding a portion of the fluid from theprocess line at a bleed line pressure that is lower than the processline pressure; determining a speed of sound propagating through thefluid flowing through the bleed line; determining a gas volume fractionof the fluid in the bleed line using the speed of sound; and determiningthe total gas content of the fluid flowing through the process lineusing the gas volume fraction of the fluid in the bleed line and avelocity of the fluid in the bleed line.

In yet another aspect, there is provided a method for measuring totalgas content of a fluid flowing through a process line at a process linepressure. The method comprises: bleeding a portion of the fluid from theprocess line at a bleed line pressure that is lower than the processline pressure and at a bleed line velocity that is approximately equalto a predetermined velocity; determining a speed of sound propagatingthrough the fluid flowing through the bleed line; and determining thetotal gas content of the fluid flowing through the process line as a gasvolume fraction of the fluid in the bleed line.

BRIEF DESCRIPTION OF THE DRAWING

Referring now to the Drawing wherein like items are numbered alike inthe various Figures:

FIG. 1 is a schematic diagram of an apparatus for measuring total gas ina fluid flowing within a process line.

FIG. 2 is an example of the apparatus of FIG. 1 removed from the processline.

FIG. 3 is a graphic comparison of gas and liquid velocities in a priorart birdbath type meter and the apparatus of FIG. 1.

FIG. 4 is a graphic comparison of the impact of slip on a prior artbirdbath type meter and the apparatus of FIG. 1.

FIG. 5 is a schematic diagram of the apparatus for measuring total gasin a fluid flowing within a process line, the apparatus including a GVFcorrection logic.

FIG. 6 is a schematic diagram of a method for measuring total gas in thefluid flowing within the process line.

FIG. 7 is a plot depicting the effect of flow rate on the total gasmeasured using the method of FIG. 6.

FIG. 8 is a schematic diagram of an apparatus for measuring total gas ina fluid flowing within a process line including an ultrasonic field torelease dissolved gas.

FIG. 9 is a schematic diagram of an apparatus for measuring entrainedgas in the fluid flowing within the process line.

FIG. 10 is a plot depicting test data output from the apparatus of FIG.9.

FIG. 11 is a schematic diagram of signal processing logic.

FIG. 12 is a k-w plot of data processed by the signal processing logicthat illustrates slope of the acoustic ridges.

FIG. 13 is a graph of a gas volume fraction (GVF) between 0.00001 and0.1 versus a mixture sound speed in meters per sec (m/s).

FIG. 14 is a graph of a gas volume fraction (GVF) between 0.0 and 0.1versus a mixture sound speed in meters per sec.

FIG. 15 is a block diagram of a flow logic used in the apparatus of thepresent invention.

FIG. 16 is a kω plot of data processed from an apparatus embodying thepresent invention that illustrates slope of the convective ridge, and aplot of the optimization function of the convective ridge.

DETAILED DESCRIPTION

Referring to FIG. 1, an apparatus 10 for measuring total gas in a fluid13 flowing within a process line 14 is shown. The apparatus 10 comprisesa bleed line 16 in fluid communication with the process line 14 forbleeding a portion of the fluid 13 from the process line 14 at a bleedline pressure that is lower than the process line pressure. An array 11of sensors 15 provides output signals P₁(t) . . . P_(N)(t) indicative ofacoustic pressure disturbances in the fluid 13 flowing through the bleedline 16, as may be caused by acoustic waves propagating through thefluid 13 within the bleed line 16, at different axial locations x₁ . . .x_(N) along the bleed line 16. The signals P₁(t) . . . P_(N)(t) from thearray 11 are used to determine a speed of sound propagating through thefluid 13 in the bleed line 16, which is in turn used to determine thetotal gas content of the fluid 13 in the bleed line 16. As will bediscussed in further detail hereinafter, the apparatus 10 includes atleast one means for accounting for the multiphase aspect of bubblyliquids to provide an accurate measurement of the total gas content ofthe process fluid 13. In one aspect, the total gas content of the fluid13 flowing through the process line 14 is calculated as a function ofthe gas volume fraction (GVF) of the fluid 13 in the bleed line 16 and avelocity of the fluid 13 in the bleed line 16. In another aspect, thevelocity of the fluid 13 in the bleed line 16 is adjusted to beapproximately equal to a predetermined velocity. In yet another aspect,dissolved gas in the process fluid 13 is released before the gas contentmeasurement point by applying a high intensity ultrasonic field to thefluid 13. Any or all of these means may be employed by the apparatus 10.

As used herein, total gas is the sum of the entrained gases and thedissolved gases contained with a fluid. Entrained gases are defined asthe gas present within the fluid at process conditions (i.e. pressureand temperature in the process line 14); and dissolved gases are definedas the gas that comes out of solution when the fluid is expanded fromprocess conditions to approximately atmospheric (ambient) pressure, suchas, for example, when a pulp suspension is released onto the wire of apaper machine. As used herein, a gas may be any single constituent gas(e.g., hydrogen, oxygen, etc.) or multiple constituent gas (e.g., air).As used herein, a fluid may be a single phase fluid (e.g., gas, liquidor liquid/liquid mixture) and/or a multi-phase mixture (e.g. paper andpulp slurries or other solid/liquid mixtures). The multi-phase mixturemay be a two-phase liquid/gas mixture, a solid/gas mixture or asolid/liquid mixture, gas entrained liquid or a three-phase mixture. Asused herein, a line is any a duct, conduit, pipe or the like.

The bleed line 16 is in fluid communication with the process line 14 forbleeding a portion of the fluid 13 from the process line 16 at a bleedline pressure that is lower than the process line pressure. For example,the bleed line 16 pressure may be substantially atmospheric pressure(e.g. about 14.7 pounds per square inch). The array 11 is disposed on asensing region 17 of the bleed line 16, which may be orientedvertically, such that the fluid 13 and entrained gas flow upward throughthe sensing region 17. The vertical orientation of the sensing regionprevents stratification of the mixture 13 (i.e., separation of the gasand fluid) and ensures propagation of the entrained gas through thesensing region at a relatively constant rate.

The bleed line 16 may include one or more flow control devices 18, suchas a valve, orifice, or other flow obstruction, to reduce pressure inthe bleed line from that of the process line. Fluid 13 from the bleedline 16 may be provided to a tank or drain 27, or used in a differentportion of the process. For example, in a paper pulp slurry application,the bleed line 16 may discharge into a white water tray. Alternatively,as depicted in FIG. 5, the bleed line 16 may also include one or moreadditional flow control devices 25, such as a pump, to increase fluid 13pressure from the low pressure side of the bleed line 16 and allow thefluid 13 to be injected back into the process line 14. Referring againto FIG. 1, the low pressure side of the bleed line 16 may also include arelief valve 23 to provide a means for bringing the pressure of thefluid 13 in the sensing region 17 to ambient pressure.

The spatial array 11 includes at least two pressure sensors 15 disposedat different axial locations x₁ . . . x_(N) along the sensing region 17of the bleed line 16. Each of the pressure sensors 15 provides a signalP(t) indicative of unsteady pressure within the bleed line 16 at acorresponding axial location x₁ . . . x_(N) of the bleed line 16. One ormore signal processors 19 receives the pressure signals P₁(t) . . .P_(N)(t) from the pressure sensors 15 in the array 11, and applies thesignals to signal processing logic 36 executed by the signal processor19 to determine the velocity, speed of sound (SOS), gas volume fraction(GVF), total gas, and various other parameters of the fluid 13. Thesignal processing logic 36 is described in further detail hereinafter.

While the array 11 is shown as including four sensors 15, it iscontemplated that the array 11 of pressure sensors 15 includes two ormore sensors 15, each providing a pressure signal P(t) indicative ofunsteady pressure within the bleed line 16 at a corresponding axiallocation X of the bleed line 16. For example, the array 11 may include2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,22, 23, or 24 pressure sensors 15. Generally, the accuracy of themeasurement improves as the number of sensors 15 in the array 11increases. The degree of accuracy provided by the greater number ofsensors 15 is offset by the increase in complexity and time forcomputing the desired output parameter of the flow. Therefore, thenumber of sensors 15 used is dependent at least on the degree ofaccuracy desired and the desire update rate of the output parameterprovided by the apparatus 10.

The signal processor 19 may be part of a larger processing unit 20. Forexample, the signal processor 19 may be one or more microprocessors andthe processing unit 20 may be a personal computer or other generalpurpose computer. It is contemplated that the signal processor 19 may beany one or more analog or digital signal processing devices forexecuting programmed instructions, such as one or more microprocessorsor application specific integrated circuits (ASICS), and may includememory for storing programmed instructions, set points, parameters, andfor buffering or otherwise storing data.

The signal processor 19 may output the velocity, speed of sound (SOS),gas volume fraction (GVF), total gas, and various other parameters ofthe fluid 13 as a signal 21. The signal 21 may be provided to a display24 or another input/output (I/O) device 26. The signal 21 may also beoutput to the flow control devices 18 and/or 25 (FIG. 5) for controllingthe velocity of the fluid 13 through the bleed line 16.

The I/O device 26 may accept user input parameters 48 as may benecessary for the signal processing logic 36. The I/O device 26, display24, and signal processor 19 unit may be mounted in a common housing,which may be attached to the array 11 by a flexible cable, wirelessconnection, or the like. The flexible cable may also be used to provideoperating power from the processing unit 20 to the array 11 ifnecessary.

Referring to FIG. 2, an example of the apparatus 10 is shown removedfrom the process line 14. In this example, the bleed line 16 includes asupply hose 70 (e.g., a 2 inch EPDM (Ethylene Propylene Diene Monomer)hose) coupled to a bottom end of a pipe 72 (e.g., a 2 inch O.D. plasticpipe) by way of a flange 74. The use of a plastic pipe 72 isadvantageous in that it provides more sensitivity for flow measurementby the array 11; however, other materials may be used. The supply hose70 may be about 15 to 20 feet in length to allow sufficient time for thefluid to outgas before entering the sensing region 17. A tap 71 having asmaller diameter than the hose 70 (e.g., 1 inch inside diameter tap 71)may be secured to the end of the hose 70 to enhance outgassing in thehose 70. The pipe 72 serves as the sensing region 17 and is mounted toany convenient surface by way of mounting hardware 76 such that thelongitudinal axis of the pipe 72 is vertical. A top end of the pipe 72is coupled by way of a flange 78 (e.g., a 2 inch rotating flange) to aninverted, U-shaped pipe section 80 (e.g., 2 inch O.D. steel pipe). Therelief valve 23 is in fluid communication with the pipe section 80, anda discharge hose 82 (e.g., a 2 inch EPDM hose) is fitted to a dischargeend of the pipe section 80.

The array 11 is disposed around the pipe 72, and includes a housing 84that protects the sensors 15 (FIG. 1) in the array 11. The array 11 iscoupled to the processing unit 20 by a cable 86, which provides thesignals P₁(t) . . . P_(N)(t) (FIG. 1) from the array 11 to theprocessing unit 20, and a cable 88 may be used to provide output signalsfrom the processing unit 20 to a remote computer device. The array 11and processing unit 20 may include, for example, a SONARtrac™ total airmeter, which is commercially available from CiDRA Corporation ofWallingford, Conn. Advantageously, the example apparatus 10 of FIG. 2may be shipped substantially in the assembled state shown, thus allowingthe end user to install the apparatus 10 by simply mounting the pipe andprocessing unit, connecting the supply hose to a process line 14 (FIG.1), and directing the return line to a low back pressure discharge(e.g., a drain, tank, white water tray, or the like).

Referring again to FIG. 1, in operation, a small amount of fluid 13 fromthe process line 14 is bled off the process line 14 either continuously,periodically, or upon demand, and the pressure of the fluid 13 isreduced to approximately atmospheric pressure in the bleed line 16. Oncethe pressure of the fluid 13 is reduced, any dissolved gas in the fluid13 is liberated from the fluid 13 and becomes entrained gas. Thus, ameasurement of the gas volume fraction (GVF) of the fluid 13 in thebleed line 16 provides the total gas measurement of the fluid 13 in theprocess line 14.

However, as the velocity of the fluid 13 sample is reduced in the bleedline 16, a situation can be created wherein gas velocity (relative tothe pipe) is appreciably faster than liquid velocity. More specifically,in a vertical column, the buoyancy force of bubbles in the liquid phasecause the bubbles to rise faster than the liquid, a phenomenon known asslippage.

Bubbles tend to rise faster than the liquid phase of a mixture by whatis often termed the “terminal velocity” of the bubble. The terminalvelocity is the speed at which a bubble would rise in a liquid at rest.Since the terminal velocity represents a balance of the buoyancy force,which scales with the volume of the bubble and the drag force, whichscales with the cross-sectional area of the bubble, the terminalvelocity is somewhat bubble size dependent. Large bubbles rise fasterthan small bubbles. Despite this dependence, it is often reasonable toapproximate bubble rise velocity independent of the size of the bubbles.For low consistency pulp suspensions, the bubble rise velocity tends tobe approximately 0.3 to 0.8 ft/sec.

Other factors that cause the mean rise velocity of bubbles to differfrom that of the liquid include the sometimes observed tendency for thebubbles to congregate near the centerline of a pipe where the velocityof the flow can be 20 to 25% greater than the volumetrically averagedflow velocity.

The combination of these effects have lead to the generally acceptedmodel for gas velocity in a bubbly mixture in a vertical tube having theform:ν_(gas)=αν_(liq)+ν_(bubble)   (1)where ν_(gas) is the velocity of gas in the sensing region 17 (relativeto the sensing region 17), ν_(bubble) is the terminal velocity of thebubbles in the sensing region 17, ν_(liquid) is the velocity of theliquid in the sensing region 17 (relative to the sensing region 17), andα is an empirically or analytically determined parameter.

The effect of this slip between the liquid and gas phases can have asignificant impact of the relationship between the actual GVF of thefluid input into the bleed line 16 (GVF_(input)) and the measured GVF inthe bleed line 16 (GVF_(InSitu)). The relation between the input andin-situ gas volume fraction is given by: $\begin{matrix}{{GVF}_{input} \equiv \frac{Q_{gas}}{Q_{gas} + Q_{liq}}} & (2) \\{{GVF}_{insitu} \equiv \frac{Q_{gas}}{Q_{gas} + {Q_{liq}\left( \frac{v_{gas}}{v_{liq}} \right)}}} & (3)\end{matrix}$

A comparison of equations 2 and 3 shows that, as the ratio between thevelocity of the gas phase (ν_(gas)) and the velocity of liquid phase(ν_(liquid)) departs from unity, so too does the ratio between themeasured GVF (GVF_(InSitu)) and the actual GVF (GVF_(input)).

In prior art air meters, such slippage will result in an inaccuratereading of total, entrained, and/or dissolved air. For example, in aso-called birdbath type of air meter, which is depicted in FIG. 3,aerated fluid 13 flows from the process line 14 into the bottom of alarge tank 90 (e.g. a cylindrical tank 14 inches in diameter orgreater), which is maintained at about atmospheric pressure. The fluid13 flows upward in the tank 90 and overflows the edges of the tank 90 oris otherwise discharged at a predetermined tank level. As the fluid 13flows upward through the tank 90, dissolved gas in the fluid 13 isreleased and becomes entrained gas bubbles 92. During this process, theweight of the volume of fluid 13 in the tank 90 is monitored. The weightof the tank 90 provides an indication of the amount of gas in the tank90 and, therefore, the total gas in the process line 14. However, wherethe velocity of the gas is higher than the velocity of the liquid, thismeasurement may be inaccurate. For example, a 14 inch O.D. birdbathhaving a fluid feed of about 10 gpm will provide a liquid velocity ofabout 0.05 fps and a gas velocity of about 0.15 fps, which results in aratio GVF_(InSitu)/GVF_(input) of about 0.3. Moreover, the measurementis highly sensitive to the feed rate of the fluid 13 into the tank. Thatis, when the bubble velocity is higher than the fluid velocity, theweight reading will be greater than when the bubble velocity isapproximately equal to the fluid velocity, even though the total gas inthe liquid 13 from the process line 14 remains unchanged. As can be seenin FIG. 4, for example, the present inventors have determined that afluid 13 flow rate of 10 gpm through a 14 inch O.D. birdbath results ina ratio GVF_(InSitu)/GVF_(input) of about 0.5, while a fluid 13 flowrate of 50 gpm through the 14 inch O.D. birdbath results in a ratioGVF_(InSitu)/GVF_(input) of about 0.18.

Referring again to FIG. 1, one means for accounting for the multiphaseaspect of bubbly liquids to provide an accurate measurement of the totalgas content of the process fluid 13 is to adjust the velocity of thefluid 13 in the sensing region 17 to a predetermined value. For example,the velocity of the fluid 13 in the bleed line 16 may be adjusted suchthat the velocity of the liquid in the sensing region 17 (v_(liquid)),measured as the velocity of the fluid 13 mixture, is greater than theestimated or measured terminal velocity of the bubbles in the sensingregion 17 (v_(bubble)). Preferably the ratio v_(liquid)/v_(bubble) isgreater than or equal to about 4/1, and more preferably greater than orequal to about 10/1. As a result, the velocity of the gas phase and thevelocity of the liquid phase will be at maintained at about unity, andthe GVF_(InSitu) and the GVF_(input) will be approximately equal. Whilehigher ratios are believed to provide more accurate results, it iscontemplated that mechanical issues may limit the ratios that can beused for a particular application. For example, the length of inlettubing (e.g., tube 70 of FIG. 2) needed to provide sufficient outgassingof dissolved fluids may be prohibitive for higher fluid velocities. Inanother example, the residency time required for sensing may beprohibitive for higher fluid velocities. Because of such mechanicallimitations, it is believed that ratios greater than about 25/1 are lesspreferred. One will appreciate that the ratio could be higher by overcoming the mechanical limitations, for example, extending the supplyhose or employing ultrasonic source 94 shown in FIG. 8.

To accomplish the desired ratio v_(liquid)/v_(bubble), the velocity ofthe fluid 13 in the sensing region 17 of the bleed line 16 may beadjusted by the selection of the size of the sensing region 17 and otherportions of the bleed line 16 and/or the setting of the various flowcontrol devices 18 and 25 in fluid communication with the bleed line 16.

For example, it has been determined that for aerated pulp suspensions, asensing region sized to provide a liquid velocity of about 2.0 fps,provides a total gas meter that is insensitive to slippage over a flowrate range from between about 10 gpm to about 50 gpm. Thus, the sensingportion of the bleed line 17 may be designed to provide these flowparameters prior to installation of the apparatus 10. As shown in FIG.3, for example, maintaining a fluid 13 flow of about 10 gpm through a 2inch O.D. sensing region 17 provides a liquid velocity of about 2 fpsand a gas velocity of about 2.1 fps, which results in a ratioGVF_(InSitu)/GVF_(input) of about 1. Accordingly, the GVF_(InSitu)measurement more accurately reflects GVF_(input). In addition, as shownin FIG. 4, because the apparatus 10 may be designed to have a sensingregion with a relatively small chamber diameter as compared to the priorart birdbath design (e.g., 2 inch O.D. versus 14 inch O.D.), theapparatus 10 is also less sensitive to feed rate than the birdbath typemeter. For example, with a 2 inch O.D. sensing region 17, a fluid 13flow rate of 10 gpm results in a ratio GVF_(InSitu)/GVF_(input) of about1, while a fluid 13 flow rate of 50 gpm results in a ratioGVF_(InSitu)/GVF_(input) of about 0.9. This is much more insensitive tochanges in flow rate than the previously described 14 inch O.D. birdbathtype meter, which resulted in GVF_(InSitu)/GVF_(input) ratios of betweenabout 0.5 to about 0.18 for the same flow rate range. Maintainingsufficiently high velocities also avoids problems associated withstratification of the fluid 13 mixture and the problems associated witheither the liquid of gas phases “holding up” in the process line 14.

Referring again to FIG. 1, in lieu of, or in addition to, designmodifications to the bleed line 16, the flow control device 18 may beused to adjust the velocity of the fluid 13 in the bleed line 16 afterinstallation of the apparatus 10. It is contemplated that, suchadjustments may be made manually, by field personnel, or automaticallyby flow control device 18 in response to signals from the signalprocessor 19. In the latter case, the signal processor 19 would sensethe fluid 13 velocity using the array of sensors 15, as will bediscussed hereinafter, and adjust the flow control device 18 in responseto the sensed velocity. Alternatively, the flow control device 18 may becontrolled by a device other than the signal processor 19 that sensesvelocity in the bleed line 16 and provides control signals to the device18 in response to the sensed velocity.

FIGS. 5 and 6 depict another means for accounting for the multiphaseaspect of bubbly liquids to provide an accurate measurement of the totalgas content of the process fluid 13, which may be incorporated by thesignal processor 19. In the embodiment of FIGS. 5 and 6, the signalprocessor applies a GVF correction logic 38 to the GVF determined by thesignal processing logic 36. More specifically, the speed at which lowfrequency sound waves propagate within the fluid 13 in the sensingregion 17 of the bleed line 16 is measured in the sensing region 17 byapplying signals output from the array 11 (block 52 of FIG. 6) to thesignal processing logic 36. Other parameters of the fluid 13 in thesensing region are also measured or estimated. For example, the pressureand temperature in the sensing region 17 is measured or estimated (block54). Also, the volumetric flow velocity of the fluid 13 in the sensingregion 17 is measured by way of the signal processing logic 36, as willbe described hereinafter, or by a separate velocity sensing apparatus(block 56). The signal processor applies the signal processing logic 36to the speed of sound (SOS) measurement, along with knowledge of thepressure and gross fluid 13 properties, to determine the in-situ GVF(block 58). The flow velocity measurement, along with knowledge of themultiphase behavior of bubbly liquids, enables the signal processor 19to provide an accurate determination of the relationship between thesought input GVF of the fluid 13 in the process line 14 and the measuredin-situ GVF of the fluid 13 within the bleed line 16, thus allowing anaccurate input GVF to be determined (block 60). The calculated input GVFmay then be provided by the signal processor 19 as an output signal 21(block 62).

Rearranging the above equations (1), (2), and (3), and inserting therelationship between the gas and liquid velocity, the sought input GVFcan be expressed in terms of the measured in-situ GVF and the measuredliquid velocity. $\begin{matrix}{{GVF}_{input} = \frac{1}{1 + \frac{1 - {GVF}_{insitu}}{\left( \frac{{\alpha\quad v_{liq}} + v_{bubble}}{v_{liq}} \right){GVF}_{insitu}}}} & (4)\end{matrix}$The relation is dependent to some degree on the slip model parameters,namely α and v_(bubble), however, these can be derived analytically ordetermined empirically. Equation (4) may be applied as the GVFcorrection logic 38 by the signal processor 19 (block 60 of FIG. 6) tocalculate the input GVF using the in-situ GVF determined by the signalprocessing logic 36 and the volumetric flow velocity of the fluid 13 inthe sensing region 17 measured by way of the signal processing logic 36or by a separate velocity sensing apparatus.

In this aspect of the invention, the flow velocity measurement isprimarily used to account for the slip effect between the gas bubblesand the fluid in the vertical sensing region 17 of the bleed line 16.Furthermore, it has a secondary benefit of being useful in estimatingflow related back pressure building up in the sensing pipe as well ascorrecting the measured propagation velocity of the acoustic wave forthe bulk velocity motion of the fluid itself.

FIG. 7 shows test data measured from a total gas meter employing themethod of FIG. 6. The Total gas meter measured the velocity of theliquid and the sound speed of the mixture. The input GVF was inferredfrom these two measurements and a slip model as developed above. Themodel used α=1 and a v_(bubble) of 0.9. As shown in FIG. 7, the inferredgas volume fraction of about 13% is shown to be insensitive to thevelocity of the mixture through the apparatus 10. In other words, asflow rate of the fluid 13 through the apparatus 10 changed (over a rangeof about 5 gpm to about 30 gpm), the measured GVF_(input) remainedunchanged.

FIG. 8 depicts another means for accounting for the multiphase aspect ofbubbly liquids to provide an accurate measurement of the total gascontent of the process fluid 13. In the embodiment of FIG. 8, thedissolved gas in the process fluid 13 is released before the gas contentmeasurement point (e.g., the sensing region 17) by applying a highintensity ultrasonic field 92 to the fluid 13. The field 92 generatesstrong local pressure variations within the fluid 13 thus releasing thedissolved gas. While not wanting to be bound by theory, it is believedthat the release of the gas is at least partially caused by thevibrating of the fluid 13 by the ultrasonic field 92, it is alsobelieved that the ultrasonic field 92 causes a combining of the microbubbles into macro bubbles minimizing the gas/liquid surface so that thegas does not dissolve back easily. Use of the ultrasonic field 92 helpsto ensure that any dissolved gas is released from the liquid and,thereby, helps to provide a more accurate reading by the apparatus 10 oftotal air in the process line 14.

The high intensity ultrasonic field 92 can be generated by continuouswave, noise, frequency swept or pulsed ultrasound transmission appliedby one or more ultrasonic sensor 94. The ultrasonic sensors 94 can beeither clamped-on the bleed line 16 or directly in contact with theprocess fluid 13. While the embodiment of FIG. 8 depicts the use of theultrasonic field with the apparatus 10, it is contemplated that theultrasonic field may be used in any application where it is necessary torelease dissolved gas from a liquid. For example, the ultrasonic field92 can happen either in a batch sample volume or a continuouslybypassing flow. The treatment of batch can happen in same volume as agas measurement. Advantageously, the use of the ultrasonic field 92provides for a fast measurement response by the apparatus 10, reducesany measurement drifts that may be caused by changes in mechanicalfrictions in the bleed line 16, and requires little or no maintenance.

Referring again to FIG. 1, the sensors 15 may include electrical straingages, optical fibers and/or gratings, ported sensors, ultrasonicsensors, among others as described herein, and may be attached to thepipe 14 by adhesive, glue, epoxy, tape or other suitable attachmentmeans to ensure suitable contact between the sensor and the pipe 14. Thesensors 15 may alternatively be removable or permanently attached viaknown mechanical techniques such as mechanical fastener, spring loaded,clamped, clam shell arrangement, strapping or other equivalents.Alternatively, strain gages, including optical fibers and/or gratings,may be embedded in a composite pipe to form the vertical sensing region17. If desired, for certain applications, gratings may be detached from(or strain or acoustically isolated from) the sensing region 17 ifdesired. It is also contemplated that any other strain sensing techniquemay be used to measure the variations in strain in the sensing region17, such as highly sensitive piezoelectric, electronic or electric,strain gages attached to or embedded in the sensing region 17.

In various embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensorsand it may measure the unsteady (or dynamic or ac) pressure variationsinside the sensing region 17 by measuring the pressure levels inside thesensing region 17. In one embodiment of the present invention, thesensors 15 comprise pressure sensors manufactured by PCB Piezotronics ofDepew, N.Y. For example, in one pressure sensor there are integratedcircuit piezoelectric voltage mode-type sensors that feature built-inmicroelectronic amplifiers, and convert the high-impedance charge into alow-impedance voltage output. Specifically, a Model 106B manufactured byPCB Piezotronics is used which is a high sensitivity, accelerationcompensated integrated circuit piezoelectric quartz pressure sensorsuitable for measuring low pressure acoustic phenomena in hydraulic andpneumatic systems. It has the unique capability to measure smallpressure changes of less than 0.001 psi under high static conditions.The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001psi).

The sensors 15 may incorporate a built-in MOSFET microelectronicamplifier to convert the high-impedance charge output into alow-impedance voltage signal. The sensors 15 may be powered from aconstant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply.

Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

The output characteristic of piezoelectric pressure sensor systems isthat of an AC-coupled system, where repetitive signals decay until thereis an equal area above and below the original base line. As magnitudelevels of the monitored event fluctuate, the output remains stabilizedaround the base line with the positive and negative areas of the curveremaining equal.

Furthermore it is contemplated that each of the sensors 15 may include apiezoelectric sensor that provides a piezoelectric material to measurethe unsteady pressures of the fluid 13. The piezoelectric material, suchas the polymer, polarized fluoropolymer, PVDF, measures the straininduced within the process pipe 14 due to unsteady pressure variationswithin the fluid 13. Strain within the sensing region 17 is transducedto an output voltage or current by the attached piezoelectric sensors15.

The PVDF material forming each piezoelectric sensor 15 may be adhered tothe outer surface of a steel strap that extends around and clamps ontothe outer surface of the sensing region 17. The piezoelectric sensingelement is typically conformal to allow complete or nearly completecircumferential measurement of induced strain. The sensors can be formedfrom PVDF films, co-polymer films, or flexible PZT sensors, similar tothat described in “Piezo Film Sensors technical Manual” provided byMeasurement Specialties, Inc. of Fairfield, N.J., which is incorporatedherein by reference. The advantages of this technique are the following:

-   -   Non-intrusive flow rate measurements    -   Low cost    -   Measurement technique requires no excitation source. Ambient        flow noise is used as a source.    -   Flexible piezoelectric sensors can be mounted in a variety of        configurations to enhance signal detection schemes. These        configurations include a) co-located sensors, b) segmented        sensors with opposing polarity configurations, c) wide sensors        to enhance acoustic signal detection and minimize vortical noise        detection, d) tailored sensor geometries to minimize sensitivity        to pipe modes, e) differencing of sensors to eliminate acoustic        noise from vortical signals.    -   Higher Temperatures (140 C) (co-polymers)

FIG. 9 depicts an apparatus 100 for measuring entrained gas in the fluid13 flowing within the process line 14. In this embodiment, the apparatus10 of FIG. 1 is used in conjunction with a similar apparatus 10′ havingits array 11′ of sensors 15′ arranged to sense acoustic pressuredisturbances in the fluid 13 flowing through the process line 14, as maybe caused by acoustic waves propagating through the fluid 13 within theprocess line 14. The signal processor 19 receives the pressure signalsP₁(t)′ . . . P_(N)(t)′ from the pressure sensors 15′ in the array 11′,and applies the signals to logic 36 executed by the signal processor 19to determine the velocity, speed of sound (SOS), gas volume fraction(GVF), and various other parameters of the fluid 13 in the process line14. Also, the signal processor 19 receives the pressure signals P₁(t) .. . P_(N)(t) from the pressure sensors 15 in the array 11, and, usingone or more of the above-described means for providing an accuratemeasurement of the total gas content of the process fluid 13 describedabove, applies the signals to logic 36 and 38 executed by the signalprocessor 19 to determine the velocity, speed of sound (SOS), input gasvolume fraction (GVF_(input)), and various other parameters of the fluid13 in the bleed line 16.

As described in U.S. patent application Ser. No. 10/762,409, filed Oct.7, 2004, which is incorporated by reference herein in its entirety, theGVF determined using the pressure signals P₁(t)′ . . . P_(N)(t)′ is theGVF of entrained air in the process line 14 (GVF_(Entrained Air)), whilethe GVF determined using the pressure signals P₁(t) . . . P_(N)(t) fromthe bleed line is the GVF of total gas in the process line 14(GVF_(input)). Accordingly, the GVF of dissolved gas in the process line14 (GVF_(dissolved gas)) may be determined by the signal processor 19using the equation:GVF _(dissolved gas) =GVF _(Input) −GVF _(Entrained Air)   (5)

Referring to FIG. 10, a graph of test data acquired using an apparatus100 of FIG. 9. The plot near the top of the graph of FIG. 10 depicts thetotal air measurement (GVF_(Input)) as a function of time as provided bythe apparatus 10 of FIG. 9. The plot near the bottom of the graphdepicts the entrained air measurement (GVF_(Entrained Air)) as afunction of time provided by the apparatus 10′ of FIG. 9. A comparisonof these two plots reveals a difference of about 3.5% GVF betweenGVF_(Input) and GVF_(Entrained Air). As described with reference toequation (5) above, this difference represents the amount of dissolvedgas in the process fluid (GVF_(dissolved gas)). Thus, the apparatus 100has shown the ability to accurately provide dissolved gas measurements.

Signal Processing Logic—Entrained Gas Measurement

The example described herein uses the speed at which sound propagateswithin a conduit to measure entrained gas in the fluid. The apparatusmeasures the speed at which acoustic wave propagating in the processpiping to determine the total gas in the process line 14. The acousticwave can be generated by a pump or other device disposed in the pipingsystem, or generated simply by the mixture/fluid flowing through theprocess line 14 and bleed line 16, all of which provide a passiveacoustic source. Alternatively, the apparatus 10 may include an activeacoustic source that injects an acoustic wave into the flow such as bycompressing, vibrating and/or tapping the process line 14 or bleed line16, to name a few examples.

This approach may be used with any technique that measures the soundspeed of the fluid. However, it is particularly synergistic with sonarbased volumetric flow meters such as described in U.S. patentapplication, Ser. No. 10/007,736 (CiDRA's Docket No. CC-0122A), in thatthe sound speed measurement, and thus gas volume fraction measurement,can be accomplished using the same hardware as that required for thevolumetric flow measurement. It should be noted, however, that the gasvolume fraction (GVF) measurement could be performed independently of avolumetric flow measurement, and would have utility as an importantprocess measurement in isolation or in conjunction with other processmeasurements.

Firstly, the sound speed may be measured as described in aforementionedU.S. patent applications, Ser. No. 09/344,094 (CiDRA's Docket No.CC-0066A), U.S. Ser. No. 10/007,749 (CiDRA's Docket No. CC-0066B), U.S.patent application, Ser. No. 10/349,716 filed Jan. 23, 2003 (Cidra'sDocket No. CC-0579) and/or U.S. patent application, Ser. No. 10/376,427filed Feb. 26, 2003 (Cidra's Docket No. CC-0596), all incorporatedherein by reference, using an array of unsteady pressure transducers.For a two component mixture, utilizing relations described in U.S.patent applications, Ser. No. 09/344,094 (CiDRA's Docket No. CC-0066A)and/or U.S. Ser. No. 10/007,749 (CiDRA's Docket No. CC-0066B), knowledgeof the density and sound speed of the two components and the complianceproperties of the conduit or pipe, the measured sound speed can be usedto determine the volumetric phase fraction of the two components.

As previously described, the array 11 of at least two sensors 15 locatedat two at least two locations x₁,x₂ axially along the sensing region 17(and, in the embodiment of FIG. 9, the process line 14) sense respectivestochastic signals propagating between the sensors within the line attheir respective locations. Each sensor 15 provides a signal indicatingan unsteady pressure at the location of each sensor 15, at each instantin a series of sampling instants. One will appreciate that the sensorarray 11 may include more than two pressure sensors 15 distributed atlocations x₁ . . . x_(N). The pressure generated by the acousticpressure disturbances (e.g., acoustic waves) may be measured throughstrained-based sensors and/or pressure sensors. The sensors 15 provideanalog pressure time-varying signals P₁(t),P₂(t),P₃(t), . . . P_(N)(t)to the signal processing logic 36. Referring to FIG. 11, the logic 36processes the signals P₁(t),P₂(t),P₃(t), . . . P_(N)(t) from the sensors15 to first provide output signals indicative of the speed of soundpropagating through the fluid (process flow) 13, and subsequently,provide output signals in response to pressure disturbances generated byacoustic waves propagating through the process flow 13, such asvelocity, Mach number and volumetric flow rate of the process flow 13.

The signal processor 19 receives the pressure signals from the array 11of sensors 15. A data acquisition unit 138 digitizes the pressuresignals P₁(t) . . . P_(N)(t) associated with the acoustic waves 122propagating through the pipe 14. An FFT logic 140 calculates the Fouriertransform of the digitized time-based input signals P₁(t) . . . P_(N)(t)and provides complex frequency domain (or frequency based) signalsP₁(ω),P₂(ω),P₃(ω), . . . P_(N)(ω) indicative of the frequency content ofthe input signals.

A data accumulator 142 accumulates the frequency signals P₁(ω) . . .P_(N)(ω) over a sampling interval, and provides the data to an arrayprocessor 144, which performs a spatial-temporal (two-dimensional)transform of the sensor data, from the xt domain to the k-ω domain, andthen calculates the power in the k-ω plane, as represented by a k-ωplot.

To calculate the power in the k-ω plane, as represented by a k-ω plot(see FIG. 12) of either the signals or the differenced signals, thearray processor 144 determines the wavelength and so the (spatial)wavenumber k, and also the (temporal) frequency and so the angularfrequency ω, of various of the spectral components of the stochasticparameter. There are numerous algorithms available in the public domainto perform the spatial/temporal decomposition of arrays of sensor units15.

In the case of suitable acoustic waves 122 being present in both axialdirections, the power in the k-ω plane shown in a k-ω plot of FIG. 12 sodetermined will exhibit a structure that is called an acoustic ridge150, 152 in both the left and right planes of the plot, wherein one ofthe acoustic ridges 150 is indicative of the speed of sound traveling inone axial direction and the other acoustic ridge 152 being indicative ofthe speed of sound traveling in the other axial direction. The acousticridges represent the concentration of a stochastic parameter thatpropagates through the flow and is a mathematical manifestation of therelationship between the spatial variations and temporal variationsdescribed above. Such a plot will indicate a tendency for k-ω pairs toappear more or less along a line 150, 152 with some slope, the slopeindicating the speed of sound.

The power in the k-ω plane so determined is then provided to an acousticridge identifier 146, which uses one or another feature extractionmethod to determine the location and orientation (slope) of any acousticridge present in the left and right k-ω plane. The velocity may bedetermined by using the slope of one of the two acoustic ridges 150, 152or averaging the slopes of the acoustic ridges 150, 152.

Finally, information including the acoustic ridge orientation (slope) isused by an analyzer 148 to determine the flow parameters relating tomeasured speed of sound, such as the consistency or composition of theflow, the density of the flow, the average size of particles in theflow, the air/mass ratio of the flow, gas volume fraction of the flow,the speed of sound propagating through the flow, and/or the percentageof entrained gas within the flow.

The array processor 144 uses standard so-called beam forming, arrayprocessing, or adaptive array-processing algorithms, i.e. algorithms forprocessing the sensor signals using various delays and weighting tocreate suitable phase relationships between the signals provided by thedifferent sensors, thereby creating phased antenna array functionality.In other words, the beam forming or array processing algorithmstransform the time domain signals from the sensor array into theirspatial and temporal frequency components, i.e. into a set of wavenumbers given by k=2π/λ where λ is the wavelength of a spectralcomponent, and corresponding angular frequencies given by ω=2πν.

One such technique of determining the speed of sound propagating throughthe process flow 13 is using array processing techniques to define anacoustic ridge in the k-ω plane as shown in FIG. 12. The slope of theacoustic ridge is indicative of the speed of sound propagating throughthe process flow 13. The speed of sound (SOS) is determined by applyingsonar arraying processing techniques to determine the speed at which theone dimensional acoustic waves propagate past the axial array ofunsteady pressure measurements distributed along the sensing region 17.

The logic 36 of the present embodiment measures the speed of sound (SOS)of one-dimensional sound waves propagating through the process flow 13to determine the gas volume fraction of the process flow 13. It is knownthat sound propagates through various mediums at various speeds in suchfields as SONAR and RADAR fields. The speed of sound propagating throughthe sensing region 17 and process flow 13 may be determined using anumber of known techniques, such as those set forth in U.S. patentapplication Ser. No. 09/344,094, filed Jun. 25, 1999, now U.S. Pat. No.6,354,147; U.S. patent application Ser. No. 10/795,111, filed Mar. 4,2004; U.S. patent application Ser. No. 09/997,221, filed Nov. 28, 2001,now U.S. Pat. No. 6,587,798; U.S. patent application Ser. No.10/007,749, filed Nov. 7, 2001, and U.S. patent application Ser. No.10/762,410, filed Jan. 21, 2004, each of which are incorporated hereinby reference.

While the sonar-based flow meter using an array of sensors 15 to measurethe speed of sound of an acoustic wave propagating through the mixtureis shown and described, one will appreciate that any means for measuringthe speed of sound of the acoustic wave may used to determine theentrained gas volume fraction of the mixture/fluid or othercharacteristics of the flow described hereinbefore.

The analyzer 148 of the logic 36 provides output parameters 21indicative of characteristics of the process flow 13 that are related tothe measured speed of sound (SOS) propagating through the process flow13. For example, to determine the gas volume fraction (or phasefraction), the analyzer 148 assumes a nearly isothermal condition forthe process flow 13. As such the gas volume fraction or the voidfraction is related to the speed of sound by the following quadraticequation:Ax ² +Bx+C=0wherein x is the speed of sound, A=1+rg/rl*(K_(eff)/P-1)-K_(eff)/P,B=K_(eff)/P-2+rg/rl; C=1-K_(eff)/rl*a_(meas)ˆ2); Rg=gas density,rl=liquid density, K_(eff)=effective K (modulus of the liquid andpipewall), P=pressure, and a_(meas)=measured speed of sound.

Effectively:Gas Voulume Fraction (GVF)=(−B+sqrt(Bˆ2-4*A*C))/(2*A)Alternatively, the sound speed of a mixture can be related to volumetricphase fraction (φ_(i)) of the components and the sound speed (a) anddensities (ρ) of the component through the Wood equation.$\frac{1}{\rho_{mix}a_{{mix}_{\infty}}^{2}} = {{\sum\limits_{i = 1}^{N}{\frac{\phi_{i}}{\rho_{i}a_{i}^{2}}\quad{where}\quad\rho_{mix}}} = {\sum\limits_{i = 1}^{N}{\rho_{i}\phi_{i}}}}$

One dimensional compression waves propagating within a process flow 13contained within a pipe (e.g., sensing region 17) exert an unsteadyinternal pressure loading on the pipe. The degree to which the pipedisplaces as a result of the unsteady pressure loading influences thespeed of propagation of the compression wave. The relationship among theinfinite domain speed of sound and density of a mixture; the elasticmodulus (E), thickness (t), and radius (R) of a vacuum-backedcylindrical conduit; and the effective propagation velocity (a_(eff))for one dimensional compression is given by the following expression:$\begin{matrix}{a_{eff} = \frac{1}{\sqrt{\frac{1}{a_{{mix}_{\infty}}^{2}} + {\rho_{mix}\frac{2R}{Et}}}}} & (6)\end{matrix}$

The mixing rule essentially states that the compressibility of a processflow (1/(ρa²)) is the volumetrically-weighted average of thecompressibilities of the components. For a process flow 13 consisting ofa gas/liquid mixture at pressure and temperatures typical of paper andpulp industry, the compressibility of gas phase is orders of magnitudesgreater than that of the liquid. Thus, the compressibility of the gasphase and the density of the liquid phase primarily determine mixturesound speed, and as such, it is necessary to have a good estimate ofprocess pressure to interpret mixture sound speed in terms of volumetricfraction of entrained gas.

Note: “vacuum backed” as used herein refers to a situation in which thefluid surrounding the pipe externally has negligible acoustic impedancecompared to that of the fluid internal to the pipe. For example, metercontaining a typical water and pulp slurry immersed in air at standardatmospheric conditions satisfies this condition and can be considered“vacuum-backed”.

For paper and pulp slurries, the conditions are such that for slurrieswith non-negligible amounts of entrained gas, say <0.01%, the complianceof standard industrial piping (Schedule 10 or 40 steel pipe) istypically negligible compared to that of the entrained gas.

FIGS. 13 and 14 show the relationship between sound speed and entrainedgas for slurries with pulp contents representative of the range used inthe paper and pulp industry. Referring to FIG. 13, two slurryconsistencies are shown; representing the lower limit, a pure watermixture is considered, and representing the higher end of consistencies,a 5% pulp/95% water slurry is considered. Since the effect of entrainedgas on the sound speed of the mixture is highly sensitive to thecompressibility of the entrained gas, the effect of the entrained gas isexamined at two pressures, one at ambient representing the lower limitof pressure, and one at 4 atmospheres representing a typical linepressure in a paper process. As shown, the consistency of the liquidslurry, i.e., the pulp content, has little effect on the relationshipbetween entrained gas volume fraction and mixture sound speed. Thisindicates that an entrained gas measurement could be accuratelyperformed, within 0.01% or so, with little or no knowledge of theconsistency of the slurry. The chart does show a strong dependence online pressure. Physically, this effect is linked to the compressibilityof the air, and thus, this indicates that reasonable estimates of linepressure and temperature would be required to accurately interpretmixture sound speed in terms of entrained gas volume fraction.

FIG. 13 also shows that for the region of interest, from roughly 1%entrained gas to roughly 5% entrained gas, mixture sound speeds(a_(mix)) are quite low compared to the liquid-only sound speeds. In theexample shown above, the sound speed of the pure water and the 5% pulpslurry were calculated, based on reasonable estimates of the constituentdensities and compressibilities, to be 1524 m/s and 1541 m/s,respectively. The sound speed of these mixtures with 1% to 5% entrainedgas at typical operating pressure (1 atm to 4 atms) are on the order of100 m/sec. The implication of these low sound speeds is that the mixturesound speed could be accurately determined with an array of sensors,i.e. using the methodology described in aforementioned U.S. patentapplications, Ser. No. 09/344,094 (CiDRA's Docket No. CC-0066A), and/orU.S. Ser. No. 10/007,749 (CiDRA's Docket No. CC-0066B), with an aperturethat is similar, or identical, to an array of sensors that would besuitable to determine the convection velocity, using the methodologydescribed in aforementioned U.S. patent application, Ser. No. 10/007,736(CiDRA's Docket No. CC-0122A), which is incorporated herein byreference.

Based on the above discussion, one may use a short length scale apertureto measure the sound speed.

The characteristic acoustic length scale is: λ=c/f; where c is the speedof sound in a mixture, f is frequency and λ is wavelength. If Aperture=Land if L/λ is approx. constant. ThenLwater/λwater=Lwater*f/C _(water) ≈L _(GVF) *f/c _(GVF)Therefore:L _(GVF) =Lwater(C _(GVF) /C _(water)); where GVF is gas volumefraction.Thus for SOS of water (Cwater=5,000 ft/sec), and SOS of the Gas volumefraction (C GVF=500 ft/sec) and a length aperture of L water=5 ft (whichwe have shown is sufficient to accurately measure the SOS of water), thelength aperture for a gas volume fraction L_(GVF) would be about 0.5feet.

Note that this entrained gas or gas volume fraction measurement GVFairmay be used with any flow meter or consistency meter to correct forerrors introduced into a measurement by entrained gas. In particular, anelectromagnetic flow meter will show an error when entrained gas existsin the mixture. The apparatus 10 may be used to correct for this error.In addition, a consistency meter will show an error when entrained gasexists in the mixture. The apparatus 10 may be used to correct for thiserror.

The connection between speed of sound of a two-phase mixture and phasefraction is well established for mixtures in which the wavelength of thesound is significantly larger than any inhomogenieities, i.e. bubbles,in the flow.

The mixing rule essentially states that the compressibility of a mixture(1/(ρa²)) is the volumetrically-weighted average of thecompressibilities of the components. For gas/liquid mixtures at pressureand temperatures typical of paper and pulp industry, the compressibilityof gas phase is orders of magnitudes greater than that of the liquid.Thus, the compressibility of the gas phase and the density of the liquidphase primarily determine mixture sound speed, and as such, it isnecessary to have a good estimate of process pressure to interpretmixture sound speed in terms of volumetric fraction of entrained gas.The effect of process pressure on the relationship between sound speedand entrained gas volume fraction is shown in FIG. 13.

Conversely, however, detailed knowledge of the liquid/slurry is notrequired for entrained gas measurement. Variations in liquid density andcompressibility with changes in consistency have a negligible effect onmixture sound speed compared to the presence of entrained gas. FIG. 14shows the mixture sound speed as a function of entrained gas volumefraction for two slurries, one with 0% wood fiber and the other with 5%wood fiber by volume. As shown, the relationship between mixture soundspeed and gas volume fraction is essentially indistinguishable for thetwo slurries. Furthermore, mixture sound speed is shown to an excellentindicator of gas volume fraction, especially for the trace to moderateamounts of entrained gas, from 0 to 5% by volume, typically encounteredin the paper and pulp industry.

Signal Processing Logic—Velocity Measurement

Referring to FIG. 15, an example of flow logic 36 is shown. Aspreviously described, each array of at least two sensors located at twolocations x₁,x₂ axially along the pipe 72 sense respective stochasticsignals propagating between the sensors within the pipe at theirrespective locations. Each sensor provides a signal indicating anunsteady pressure at the location of each sensor, at each instant in aseries of sampling instants. One will appreciate that each sensor arraymay include more than two sensors distributed at locations x₁ . . .x_(N). The pressure generated by the convective pressure disturbances(e.g., eddies or vortical disturbances) may be measured throughstrained-based sensors and/or pressure sensors. The sensors provideanalog pressure time-varying signals P₁(t),P₂(t),P₃(t),P_(N)(t) to theflow logic 36.

The flow logic 36 processes the signals P₁(t),P₂(t),P₃(t),P_(N)(t) tofirst provide output signals (flow parameters) indicative of thepressure disturbances that convect with the fluid (process flow) 13, andsubsequently, provide output signals in response to pressuredisturbances generated by convective waves propagating through the fluid13, such as velocity, Mach number and volumetric flow rate of theprocess flow 13. The flow logic 36 processes the pressure signals tofirst provide output signals indicative of the pressure disturbancesthat convect with the process flow 13, and subsequently, provide outputsignals in response to pressure disturbances generated by convectivewaves propagating through the process flow 13, such as velocity, Machnumber and volumetric flow rate of the process flow 13.

The flow logic 36 receives the pressure signals from the array ofsensors 15. A data acquisition unit 126 (e.g., A/D converter) convertsthe analog signals to respective digital signals. The FFT logic 128calculates the Fourier transform of the digitized time-based inputsignals P₁(t)-P_(N)(t) and provides complex frequency domain (orfrequency based) signals P₁(ω),P₂(ω),P₃(ω),P_(N)(ω) indicative of thefrequency content of the input signals. Instead of FFT's, any othertechnique for obtaining the frequency domain characteristics of thesignals P₁(t)-P_(N)(t), may be used. For example, the cross-spectraldensity and the power spectral density may be used to form a frequencydomain transfer functions (or frequency response or ratios) discussedhereinafter.

One technique of determining the convection velocity of the turbulenteddies 120 within the process flow 13 is by characterizing a convectiveridge of the resulting unsteady pressures using an array of sensors orother beam forming techniques, similar to that described in U.S. patentapplication, Ser. No. (Cidra's Docket No. CC-0122A) and U.S. patentapplication, Ser. No. 09/729,994 (Cidra's Docket No. CC-0297), filedDec. 4, 200, now U.S. Pat. No. 6,609,069, which are incorporated hereinby reference.

A data accumulator 130 accumulates the frequency signals P₁(ω)-P_(N)(ω)over a sampling interval, and provides the data to an array processor132, which performs a spatial-temporal (two-dimensional) transform ofthe sensor data, from the xt domain to the k-ω domain, and thencalculates the power in the k-ω plane, as represented by a k-ω plot.

The array processor 132 uses standard so-called beam forming, arrayprocessing, or adaptive array-processing algorithms, i.e. algorithms forprocessing the sensor signals using various delays and weighting tocreate suitable phase relationships between the signals provided by thedifferent sensors, thereby creating phased antenna array functionality.In other words, the beam forming or array processing algorithmstransform the time domain signals from the sensor array into theirspatial and temporal frequency components, i.e. into a set of wavenumbers given by k=2π/λ where λ is the wavelength of a spectralcomponent, and corresponding angular frequencies given by ω=2πν.

The prior art teaches many algorithms of use in spatially and temporallydecomposing a signal from a phased array of sensors, and the presentinvention is not restricted to any particular algorithm. One particularadaptive array processing algorithm is the Capon method/algorithm. Whilethe Capon method is described as one method, the present inventioncontemplates the use of other adaptive array processing algorithms, suchas MUSIC algorithm. The present invention recognizes that suchtechniques can be used to determine flow rate, i.e. that the signalscaused by a stochastic parameter convecting with a flow are timestationary and have a coherence length long enough that it is practicalto locate sensor units apart from each other and yet still be within thecoherence length.

Convective characteristics or parameters have a dispersion relationshipthat can be approximated by the straight-line equation,k=ω/u,

where u is the convection velocity (flow velocity). A plot of k-ω pairsobtained from a spectral analysis of sensor samples associated withconvective parameters portrayed so that the energy of the disturbancespectrally corresponding to pairings that might be described as asubstantially straight ridge, a ridge that in turbulent boundary layertheory is called a convective ridge. What is being sensed are notdiscrete events of turbulent eddies, but rather a continuum of possiblyoverlapping events forming a temporally stationary, essentially whiteprocess over the frequency range of interest. In other words, theconvective eddies 120 is distributed over a range of length scales andhence temporal frequencies.

To calculate the power in the k-ω plane, as represented by a k-ω plot(see FIG. 16) of either the signals, the array processor 132 determinesthe wavelength and so the (spatial) wavenumber k, and also the(temporal) frequency and so the angular frequency ω, of various of thespectral components of the stochastic parameter. There are numerousalgorithms available in the public domain to perform thespatial/temporal decomposition of arrays of sensor units 15.

The present invention may use temporal and spatial filtering toprecondition the signals to effectively filter out the common modecharacteristics P_(common mode) and other long wavelength (compared tothe sensor spacing) characteristics in the pipe 14 by differencingadjacent sensors and retain a substantial portion of the stochasticparameter associated with the flow field and any other short wavelength(compared to the sensor spacing) low frequency stochastic parameters.

In the case of suitable turbulent eddies being present, the power in thek-ω plane shown in a k-ω plot of FIG. 16 shows a convective ridge 124.The convective ridge represents the concentration of a stochasticparameter that convects with the flow and is a mathematicalmanifestation of the relationship between the spatial variations andtemporal variations described above. Such a plot will indicate atendency for k-ω pairs to appear more or less along a line 124 with someslope, the slope indicating the flow velocity.

Once the power in the k-ω plane is determined, a convective ridgeidentifier 134 uses one or another feature extraction method todetermine the location and orientation (slope) of any convective ridge124 present in the k-ω plane. In one embodiment, a so-called slantstacking method is used, a method in which the accumulated frequency ofk-ω pairs in the k-ω plot along different rays emanating from the originare compared, each different ray being associated with a different trialconvection velocity (in that the slope of a ray is assumed to be theflow velocity or correlated to the flow velocity in a known way). Theconvective ridge identifier 134 provides information about the differenttrial convection velocities, information referred to generally asconvective ridge information.

The analyzer 136 examines the convective ridge information including theconvective ridge orientation (slope). Assuming the straight-linedispersion relation given by k=ω/u, the analyzer 136 determines the flowvelocity, Mach number and/or volumetric flow, which are output asparameters. The volumetric flow is determined by multiplying thecross-sectional area of the inside of the pipe with the velocity of theprocess flow.

Some or all of the functions within the flow logic 36 may be implementedin software (using a microprocessor or computer) and/or firmware, or maybe implemented using analog and/or digital hardware, having sufficientmemory, interfaces, and capacity to perform the functions describedherein.

While the present invention shows a particular meter for measuring thespeed of sound propagating through the pipe and/or the velocity of thefluid flowing through the pipe to measure the total gas, the presentinvention contemplates that any meter or means may be used to measurethe speed of sound and velocity, such as ultrasonic meters known n theart.

The apparatus 10 may provide a dual function of measuring both the gasvolume fraction of the mixture and the speed of sound propagatingthrough the mixture, which is similar to that described in U.S. patentapplication Ser. No. 10/766,440 (CC-0714), filed on Jan. 27, 2004; andU.S. patent application Ser. No. 10/875,857 (CC-0749), filed on Jun. 24,2004, which are incorporated herein by reference.

While the apparatus 10 is described as using an array of sensors tomeasure the speed of sound of an acoustic wave propagating through themixture, the scope of the invention is intended to include other ways ofmeasuring the speed of sound either known now or developed in thefuture.

It should be understood that, unless stated otherwise herein, any of thefeatures, characteristics, alternatives or modifications describedregarding a particular embodiment herein may also be applied, used, orincorporated with any other embodiment described herein.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein without departing from thespirit and scope of the present invention.

1. An apparatus for measuring total gas content of a fluid flowingthrough a process line at a process line pressure, the apparatuscomprising: a bleed line in fluid communication with the process linefor bleeding a portion of the fluid from the process line at a bleedline pressure that is lower than the process line pressure; a device fordetermining a speed of sound propagating through the fluid flowingthrough the bleed line; and at least one signal processor configured to:determine a gas volume fraction of the fluid in the bleed line using thespeed of sound, determine the total gas content of the fluid flowingthrough the process line using the gas volume fraction of the fluid inthe bleed line and a velocity of the fluid in the bleed line, andprovide an output signal indicative of the total gas content of thefluid flowing through the process line.
 2. The apparatus of claim 1,wherein the total gas content of the fluid flowing through the processline is determined using the equation:${GVF}_{input} = \frac{1}{1 + \frac{1 - {GVF}_{insitu}}{\left( \frac{{\alpha\quad v_{liq}} + v_{bubble}}{v_{liq}} \right){GVF}_{insitu}}}$3. The apparatus of claim 1, wherein the at least one signal processordetermines the velocity of the fluid in the bleed line using the outputsignals from the array of sensors.
 4. The apparatus of claim 1, whereinthe velocity of the fluid in the bleed line is adjusted to beapproximately equal to a predetermined velocity.
 5. The apparatus ofclaim 4, wherein the velocity of the fluid in the bleed line is adjustedby at least one of: a size of the bleed line and a flow control devicein fluid communication with the bleed line.
 6. The apparatus of claim 1,wherein the at least one signal processor determines an amount ofdissolved gas in the fluid flowing through the process line as adifference between a gas volume fraction of the fluid flowing throughthe process line and the total gas content of the fluid flowing throughthe process line.
 7. The apparatus of claim 1, wherein the device fordetermining the speed of sound includes: an array of sensors disposed atdifferent axial locations along a length of the bleed line, the array ofsensors being configured to provide an output signal indicative ofacoustic pressure disturbances in the fluid flowing through the bleedline at the different axial locations.
 8. An apparatus for measuringtotal gas content of a fluid flowing through a process line at a processline pressure, the apparatus comprising: a bleed line in fluidcommunication with the process line for bleeding a portion of the fluidfrom the process line at a bleed line pressure that is lower than theprocess line pressure and at a bleed line velocity that is approximatelyequal to a predetermined velocity; a device for determining a speed ofsound propagating through the fluid flowing through the bleed line; andat least one signal processor configured to: determine the total gascontent of the fluid flowing through the process line as a gas volumefraction of the fluid in the bleed line using the speed of sound, andprovide an output signal indicative of the total gas content of thefluid flowing through the process line.
 9. The apparatus of claim 8,wherein the velocity of the fluid in the bleed line is adjusted by atleast one of: a size of the bleed line and a flow control device influid communication with the bleed line.
 10. The apparatus of claim 8,wherein the velocity of the fluid in the bleed line is adjusted inresponse to a sensed velocity in the bleed line.
 11. The apparatus ofclaim 8, wherein the at least one signal processor determines an amountof dissolved gas in the fluid flowing through the process line as adifference between a gas volume fraction of the fluid flowing throughthe process line and the total gas content of the fluid flowing throughthe process line.
 12. The apparatus of claim 8, wherein the device fordetermining the speed of sound includes: an array of sensors disposed atdifferent axial locations along a length of the bleed line, the array ofsensors being configured to provide an output signal indicative ofacoustic pressure disturbances in the fluid flowing through the bleedline at the different axial locations.
 13. The apparatus of claim 8,wherein the predetermined velocity is at least about five times greaterthan an estimated bubble velocity.
 14. A method for measuring total gascontent of a fluid flowing through a process line at a process linepressure, the method comprising: bleeding a portion of the fluid fromthe process line at a bleed line pressure that is lower than the processline pressure; determining a speed of sound propagating through thefluid flowing through the bleed line; determining a gas volume fractionof the fluid in the bleed line using the speed of sound; and determiningthe total gas content of the fluid flowing through the process lineusing the gas volume fraction of the fluid in the bleed line and avelocity of the fluid in the bleed line.
 15. The method of claim 14,wherein the total gas content of the fluid flowing through the processline is determined using the equation:${GVF}_{input} = \frac{1}{1 + \frac{1 - {GVF}_{insitu}}{\left( \frac{{\alpha\quad v_{liq}} + v_{bubble}}{v_{liq}} \right){GVF}_{insitu}}}$16. The method of claim 14, further comprising: sensing acousticpressure disturbances in the fluid flowing through the bleed line atdifferent axial locations along the bleed line to provide signalsindicative of the sensed acoustic pressure disturbances; and using thesignals indicative of the sensed acoustic pressure disturbances todetermine the speed of sound propagating through the fluid flowingthrough the bleed line.
 17. The method of claim 16, further comprising:determining the velocity of the fluid in the bleed line using thesignals indicative of the sensed acoustic pressure disturbances.
 18. Themethod of claim 14, further comprising: adjusting the velocity of thefluid in the bleed line to be approximately equal to a predeterminedvelocity.
 19. The method of claim 14, further comprising: determining anamount of dissolved gas in the fluid flowing through the process line asa difference between a gas volume fraction of the fluid flowing throughthe process line and the total gas content of the fluid flowing throughthe process line.
 20. A method for measuring total gas content of afluid flowing through a process line at a process line pressure, themethod comprising: bleeding a portion of the fluid from the process lineat a bleed line pressure that is lower than the process line pressureand at a bleed line velocity that is approximately equal to apredetermined velocity; determining a speed of sound propagating throughthe fluid flowing through the bleed line; and determining the total gascontent of the fluid flowing through the process line as a gas volumefraction of the fluid in the bleed line.
 21. The method of claim 20,wherein the velocity of the fluid in the bleed line is adjusted by atleast one of: a size of the bleed line and a flow control device influid communication with the bleed line.
 22. The method of claim 20,wherein the velocity of the fluid in the bleed line is adjusted inresponse to a sensed velocity in the bleed line.
 23. The method of claim20, further comprising: determining an amount of dissolved gas in thefluid flowing through the process line as a difference between a gasvolume fraction of the fluid flowing through the process line and thetotal gas content of the fluid flowing through the process line.
 24. Themethod of claim 20, further comprising: sensing acoustic pressuredisturbances in the fluid flowing through the bleed line at differentaxial locations along the bleed line to provide signals indicative ofthe sensed acoustic pressure disturbances; and using the signalsindicative of the sensed acoustic pressure disturbances to determine thespeed of sound propagating through the fluid flowing through the bleedline.
 25. The method of claim 20, wherein the predetermined velocity isat least about five times greater than an estimated bubble velocity.